DUIYI (CLAIRE) DAI · QUANTITATIVE RESEARCH
QIS Index & Risk Lab
Systematic multi-asset strategy research, portfolio risk and index calculation.
Python · Time-series signals · Volatility control · Portfolio accounting · Risk analytics
Volatility-controlled multi-asset trend
A monthly trend signal allocates across US equities, US Treasuries and gold, with inactive allocations held in cash. A daily volatility overlay reduces risky exposure when estimated portfolio risk exceeds a 10% reference.
The comparisons separate the effects of the trend filter, volatility control and transaction costs.
Current results use simulated data. Historical-market analysis is not included in this version.
Index performance
Initial level 100, before deployment costs. The chart shows the full period; the period selector applies to the summary statistics and comparison table.
Baseline netBaseline grossSelected strategy
Strategy and sensitivity comparison
RISK
Volatility and portfolio exposure
The overlay reduces exposure without leverage. Its effect is measured against subsequent realized volatility, which can differ from the forecast.
Forecast and realized volatility
Forecast at execution versus realized volatility over the following 63 sessions. The last observations have no complete forward window.
ForecastSubsequent realized
Risky-asset exposure
Combined post-trade weight in equities, Treasuries and gold. The remainder is cash.
Component notionals
CALCULATION AUDIT
Daily index calculation
Select a date to inspect the signal, target weights and executed allocation, then reconcile asset P&L, cash interest and costs to the closing index level.
Holdings and full calculation record
Data revision example
METHODOLOGY
Rules and calculation conventions
Signal and risk control
- At each trading month end, a sleeve is active if its trailing 252-session total return is positive.
- Each active sleeve receives a base weight of one third. Inactive allocations remain in cash.
- Daily sample covariance uses 63 complete return observations. Base portfolio volatility is annualized with 252 sessions.
- Scale = min(1, 0.10 / max(base volatility, 0.01)). Target risky weights equal scaled base weights.
The 10% reference is a control input, not a guarantee of realized volatility. The overlay rebalances daily; the equal-third and trend-only comparisons rebalance monthly.
Execution and accounting
Information observed after close t determines a target executed at close t+1. Existing holdings earn the return into that execution close; new holdings first earn the t+1 to t+2 return.
Positions are marked to market and cash accrues interest before trading. Target weights refer to post-cost wealth W:
W + c Σ|wᵢW − vᵢ| = V
V is pre-trade wealth, vᵢ the existing risky notional and c the transaction-cost rate. The baseline charges 5 bps on absolute risky notional bought or sold, including initial deployment.
Timing example and cash convention
A decision after Friday 31 January 2025 closes executes on Monday 3 February. The new holdings earn Monday-to-Tuesday returns. Month ends use the complete XNYS calendar rather than the final row of an input file.
Cash assumes a 2% annual rate with ACT/360 accrual over actual calendar days. Friday-to-Monday accrual therefore covers three days. Historical cash inputs would require an official source and explicit publication availability.
Performance and risk definitions
CAGR uses elapsed calendar days / 365.25. Volatility is the sample standard deviation of daily returns × √252. Sharpe uses mean daily excess return over the same-interval cash return, divided by its sample standard deviation, × √252. Undefined values are N/A.
Maximum drawdown includes the starting capital anchor. Turnover is absolute risky notional traded / pre-trade wealth, summed over the selected period, without a one-half factor. Costs are index points. Gross and net paths are calculated separately because costs change subsequent investable wealth.
Forecast volatility uses information available at the preceding decision close. Subsequent realized volatility uses the next 63 portfolio returns and is used only for evaluation.
Data, evaluation periods and limitations
Simulated prices cover 2004–2025, with rising, falling, flat and volatility-shock regimes. The full strategy evaluation begins after the required warm-up. The simulation illustrates strategy behavior and accounting; it does not establish historical investment performance.
Development ends in 2016; held-back evaluation covers 2017–2025. Both are retrospective, and the held-back results have been inspected. Sensitivities change one baseline input at a time; no parameter selection is based on performance.
Historical-market analysis awaits suitable licensed price data and documented cash-rate availability. Historical inputs and outputs are not included in this site. A current adjusted-price snapshot would not establish a point-in-time database.
The model omits taxes, market impact and external management fees. It uses close execution and reinvestment prices; distributions and embedded fund expenses would not be counted twice. Universe choice, covariance estimation and cash assumptions limit interpretation.
This is independent research, not a live trading system or a production index. Publication status and source-rights review are recorded in the project documentation.
Code on GitHubResearch reportResults · JSONCalculation manifest
OPTION SANDBOX
European option prices and Greeks
A separate Black–Scholes illustration for a hypothetical non-distributing index. The initial level is taken from the strategy; pricing volatility is independently assumed.
Model assumptions and delta mapping
The model assumes lognormal returns, constant volatility and a constant continuously compounded risk-free rate. It is not a valuation model calibrated to the dynamic strategy. Assumed pricing volatility is distinct from forecast risk, realized volatility and the 10% control reference.
Local component exposure = position delta × index level × frozen component weight. An offsetting hedge has the opposite sign: a long call implies positive replication exposure and a negative offset; a long put reverses those signs.
The approximation ignores future allocation changes, volatility exposure, jumps, costs and liquidity. The ETF basket is not a perfect hedge. Delta is dollars per index point; gamma is dollars per index point squared.
The displayed cases are precomputed in Python. The underlying module also handles expiry and zero volatility; derivatives at payoff kinks are undefined.